ShapesDirect2 coloring, Part 1
This direct coloring formula, in jlb.ucl, lets you combine many of a single standard shape (circles, generalized ellipses, squares, rectangles, and triangles) in various ways. Use a pixel formula with it. Here’s a sample parameter set that we’ll use in the following explanation:
Ellipses1 {
::0muYXhn2NaVTvtNOQ07Gw/HI09KLy1yOuF8S3sLwGstXavTQLRJxEKKCSqE79X/OUy2RUy9D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}
Open this file in Ultra Fractal 5, adjust the size to your taste, and click on the Outside tab. We’ll look at the entries from top to bottom. For now, stay with Color Density 1 and Linear Transfer Function (experiment later).
The shape is Ellipse, Power 2.5, and there are 100 of them. (500 is the maximum.) The ellipses could be arranged in a regular two-dimensional grid or in the way this one is. Change the 100 to 1. This is a single annular ellipse. (All the shapes are annular, thought they can be fully filled in.) With Color Density 1 and Linear Transfer Function the gradient goes all the way around the shape.
A standard ellipse with center at (x0,y0) has the mathematical formula (x-x0)^2/a^2 + (y-y0)^2/b^2 = 1. The Power is 2. Generalized ellipses have the Power as variable. Powers higher than 2 result in shapes that get squarer. Powers lower than 2 result in shapes that get pointier. Experiment.
Note: for some of the Experiments you will want a large number of shapes, and for others a small number. Experiment.
Now look at the “Initial Point and its movement” block. The first ellipse has its center at (1,0). Successive ellipses can change their centers Incrementally or Randomly. The second ellipse has its center at (0.9,0) but rotated counter-clockwise by 10 degrees. Change the number of shapes to 2 to see this. Experiment.
Now look at the “Shape parameters” block. The first ellipse is 2 wide in the x direction (“a” in the formula above) and 0.75 high in the y direction (“b” in the formula above). Successive ellipses can change their shapes Incrementally or Randomly. If Incrementally, the change can be Multiplicative or Additive. In this case successive ellipses get smaller by a factor of 0.95. With the “Keep aspect ratio?” box checked, both the x size and the y size get multiplied by the same amount. If it isn’t checked, the two sizes can differ. Experiment.
Now look at the “Rotation angle and its changing” block. The x axis of the first ellipse is not rotated. Successive ellipses can have their x axes rotated Incrementally or Randomly. The second ellipse has its axis rotated counter-clockwise by 10 degrees. Experiment. Try changing -10 to 10 and changing the number of shapes to 100. Change the number of shapes back to 1.
Now look at the “Thickness of annulus and its changing” block. The first ellipse has an annulus Thickness of 0.25. Successive ellipses can change their Thicknesses Incrementally or Randomly. If Incrementally, the change can be Multiplicative or Additive. In this case each successive annulus gets smaller by a factor of 0.95. The program limits the maximum size of the annulus to the size that would fill in if Inside Edge blending is Flat (see two paragraphs later). Experiment.
Now look at the “Gradient offset and its changing” block. If the “Uniform shape color” box is checked, the shape has the same color all the way around the annulus. If the box is not checked, the shape changes colors around the annulus according to the gradient. With Color Density 1 and Linear Transfer Function, all the gradient is used exactly. Experiment. The first ellipse has Gradient Offset of 0.75. Successive ellipses can change their Gradient Offsets Incrementally or Randomly. In this case each successive ellipse has its gradient shifted by an additional 0.1. Note that gradients are considered to go from 0 to 1. Gradients that vary smoothly and have the same color at 0 and 1 are usually better.
Now look at the “Edge blending” block. Set the number of shapes to 1. If the Blend type is Flat, the color is uniform across the annulus (not along the length of it). Either the outside edge or the inside edge or both edges can be blended into a color. The sharpness of the blending is determined by the blend power. A power of 2 is reasonable. Higher powers give sharper edges, approaching flat. Powers lower than 2 can give odd results. You can make the blend colors the same as the background color or not. The Outside and Inside blend colors do not have to be the same. If the “Keep hue?” box is checked, the local hue of the annulus does not change, but the saturation and luminosity do. (The effect of this can’t be seen when blending to white, gray, or black.) Experiment.
Finally (finally!) for part 1:
Now look at the “Overlap coloring” block. If shapes overlap, the resulting color can be an average of from 1 to all of the overlapping shapes. Experiment.
The remaining blocks will be covered in Part 2.
ShapesDirect2 coloring, Part 1
This direct coloring formula, in jlb.ucl, lets you combine many of a single standard shape (circles, generalized ellipses, squares, rectangles, and triangles) in various ways. Use a pixel formula with it. Here’s a sample parameter set that we’ll use in the following explanation:
Ellipses1 {
::0muYXhn2NaVTvtNOQ07Gw/HI09KLy1yOuF8S3sLwGstXavTQLRJxEKKCSqE79X/OUy2RUy9D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}
Open this file in Ultra Fractal 5, adjust the size to your taste, and click on the Outside tab. We’ll look at the entries from top to bottom. For now, stay with Color Density 1 and Linear Transfer Function (experiment later).
The shape is Ellipse, Power 2.5, and there are 100 of them. (500 is the maximum.) The ellipses could be arranged in a regular two-dimensional grid or in the way this one is. Change the 100 to 1. This is a single annular ellipse. (All the shapes are annular, thought they can be fully filled in.) With Color Density 1 and Linear Transfer Function the gradient goes all the way around the shape.
A standard ellipse with center at (x0,y0) has the mathematical formula (x-x0)^2/a^2 + (y-y0)^2/b^2 = 1. The Power is 2. Generalized ellipses have the Power as variable. Powers higher than 2 result in shapes that get squarer. Powers lower than 2 result in shapes that get pointier. Experiment.
Note: for some of the Experiments you will want a large number of shapes, and for others a small number. Experiment.
Now look at the “Initial Point and its movement” block. The first ellipse has its center at (1,0). Successive ellipses can change their centers Incrementally or Randomly. The second ellipse has its center at (0.9,0) but rotated counter-clockwise by 10 degrees. Change the number of shapes to 2 to see this. Experiment.
Now look at the “Shape parameters” block. The first ellipse is 2 wide in the x direction (“a” in the formula above) and 0.75 high in the y direction (“b” in the formula above). Successive ellipses can change their shapes Incrementally or Randomly. If Incrementally, the change can be Multiplicative or Additive. In this case successive ellipses get smaller by a factor of 0.95. With the “Keep aspect ratio?” box checked, both the x size and the y size get multiplied by the same amount. If it isn’t checked, the two sizes can differ. Experiment.
Now look at the “Rotation angle and its changing” block. The x axis of the first ellipse is not rotated. Successive ellipses can have their x axes rotated Incrementally or Randomly. The second ellipse has its axis rotated counter-clockwise by 10 degrees. Experiment. Try changing -10 to 10 and changing the number of shapes to 100. Change the number of shapes back to 1.
Now look at the “Thickness of annulus and its changing” block. The first ellipse has an annulus Thickness of 0.25. Successive ellipses can change their Thicknesses Incrementally or Randomly. If Incrementally, the change can be Multiplicative or Additive. In this case each successive annulus gets smaller by a factor of 0.95. The program limits the maximum size of the annulus to the size that would fill in if Inside Edge blending is Flat (see two paragraphs later). Experiment.
Now look at the “Gradient offset and its changing” block. If the “Uniform shape color” box is checked, the shape has the same color all the way around the annulus. If the box is not checked, the shape changes colors around the annulus according to the gradient. With Color Density 1 and Linear Transfer Function, all the gradient is used exactly. Experiment. The first ellipse has Gradient Offset of 0.75. Successive ellipses can change their Gradient Offsets Incrementally or Randomly. In this case each successive ellipse has its gradient shifted by an additional 0.1. Note that gradients are considered to go from 0 to 1. Gradients that vary smoothly and have the same color at 0 and 1 are usually better.
Now look at the “Edge blending” block. Set the number of shapes to 1. If the Blend type is Flat, the color is uniform across the annulus (not along the length of it). Either the outside edge or the inside edge or both edges can be blended into a color. The sharpness of the blending is determined by the blend power. A power of 2 is reasonable. Higher powers give sharper edges, approaching flat. Powers lower than 2 can give odd results. You can make the blend colors the same as the background color or not. The Outside and Inside blend colors do not have to be the same. If the “Keep hue?” box is checked, the local hue of the annulus does not change, but the saturation and luminosity do. (The effect of this can’t be seen when blending to white, gray, or black.) Experiment.
Finally (finally!) for part 1:
Now look at the “Overlap coloring” block. If shapes overlap, the resulting color can be an average of from 1 to all of the overlapping shapes. Experiment.
The remaining blocks will be covered in Part 2.
